THEORY OF RELATIVITY 
287 
netic, or better, the ‘electromagnetic field' that is the physical 
reality; and -this finds its expression as a metric property of 
space; mathematically represented by a set of differential equa- 
tions involving twenty functions which finding their place in 
these equations express the curvature of the space-time con- 
tinuum just as the Rieman ‘curvature components' do in three 
dimensional space. If these twenty functions were zero, either 
the gravitational field would not be present, according to Ein- 
stein, or it could be ‘completely' removed by a proper change of 
frame of reference. But we know that it can not be removed ex- 
cept within a very small region. This means that there are some 
essential ‘curvature components' that can not be done away with 
by any choice of frame of reference ; in other words the twenty 
curvature components are not ‘individually' equal to zero. 
Einstein now reasoned that there must be some mathematical 
relation corresponding to the physical properties of space-time 
independent of the choice of frame of reference; and here it is 
the genius of Einstein that makes the brilliant guess that certain 
‘linear functions' of these curvature components are zero out- 
side of matter and equal to a similar group of functions within 
matter involving internal dynamical properties of matter itself, 
of which the electron theory will give us more and more infor- 
mation as time goes on. 
The attempt has been made by Weyl and others to include 
the electro-magnetic field side by side with or intrinsically con- 
nected with the gravitational field, but Einstein says that such 
considerations will not bring us nearer to the true’ solution of 
the problem. According to him a theory in which the gravita- 
tional field and the electromagnetic field enter as an essential 
entity would be much more preferable. 
Prof. Einstein has published a paper in the “Sitz. Ber. d. 
Preuss. Akad," 1923, in which he presents this master problem 
of “gravitation-cum-electro-magnetism" expressed in forty dif- 
ferential equations characteristic in containing besides the funda- 
mental covariant tensor g/xv of the gravitational field the funda- 
mental covarient tensor Ffj.v of the electromagnetic field, includ- 
ing of course also matter, as we usually do not think of it, namely 
as nuclei or centres of electromagnetic action; or electrons and 
protons exhibiting respectively negative and positive charges of 
electricity. 
